Backward Blow-up Estimates and Initial Trace for a Parabolic System of Reaction-Diffusion

Abstract

In this article we study the positive solutions of the parabolic semilinear system of competitive typewhere Ω is a domain of R N , and p, q > 0, pq = 1. Despite of the lack of comparison principles, we prove local upper estimates in the superlinear case pq > 1 of the formin ω × (0, T 1 ) , for any domain ω ⊂⊂ Ω and T 1 ∈ (0, T ) , and C = C(N, p, q, T 1 , ω). For p, q > 1, we prove the existence of an initial trace at time 0, which is a Borel measure on Ω. Finally we prove that the punctual singularities at time 0 are removable when p, q ≧ 1 + 2/N.